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October 23, 2007


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Wow, Ralph, talk about flamebait. Couldn't there be genuine philosophical reasons for rejecting deotnic logic? Many are neither lazy nor technically incompetent but find, rightly or wrongly, that most systems of deontic logic presuppose controversial normative judgments. I don't think ethics is a ghetto. (Do you?) Nor do I think that ethical question must be framed in technical apparatus if they are to be clear. Which is not to say that technology can help when required.

Hi Ralph,
But! The principles of deontic logic that one accepts are not independent of substantive moral theory. (Sayre-McCord has good paper on this in Nous in the 80s if I remember right.) The idea that logic can crank out relatively uncontroversial 'results' that are then accepted as 'proved' is a common philosophical error and delusion. (I suspect that this error is more prevalent in the UK because of the lesser influence of Quine.) People love the idea that one can shortcut one's way through hard philosophical problems; hence the temptation to appeal to other disciplines and also to rely on formal methods. But you can almost always catch the formalist merely helping themselves to some substantive principle, and concealing it in the formalism. Hence the suspicion! The claim that logic has a 'limited' role is right, not shocking, in my view. It does not say it has no role. (I have been reading the great Neurath recently, which may show.)
Cheers, Nick

OK, I'm sorry. Mark and Nick are right that my post was unnecessarily inflammatory (or "flamebait" as Mark puts it -- thanks for introducing me to that word!)

Clearly, Mark and Nick are right it needn't be laziness or lack of technical expertise that explains the neglect of deontic logic. It may just be the acceptance of certain philosophical falsehoods. E.g., perhaps some metaethicists neglect deontic logic because they believe that the "logic" of a concept must be completely neutral on all matters on which competent theorists disagree, or that the process of arguing for a certain account of the "logic" of a concept is independent of any "substantive" theorizing. Then because they find that many of the proposed principles of deontic logic are controversial, they take this as a reason for "rejecting" deontic logic (rather as if someone who saw that the S5 axiom of modal logic is controversial were to conclude that modal logic should be "rejected" ...).

Of course I don't think that ethics is a ghetto. But I am troubled by the fact that an increasing number of philosophers seem to operate as though those outside moral philosophy have no need to pay any attention to what is going on inside moral philosophy, and vice versa.

Perhaps it would help if the claim that deontic logic should be employed more within ethics could be supported by some examples of good articles which make headway with -- and because of -- its use.

Because if a set of technical tools doesn't, at the end of the day, make an argument any better or much clearer, then I'm not sure if we should be shocked that people don't put in the effort to master those tools.

I would imagine that people's scepticism about deontic logic is probably motivated more by a sense of redundancy, than by a suspicion of substantive bias.

(This is an open question, not a roundabout way of saying deontic logic is indeed redundant).

Technically, the debate was initiated by Michael Steven Green's post at PrawfsBlawg (where it remains 'rumbling away'). In addition, he earlier initiated a debate on Hans Kelsen's legal theory that was, as in this case, picked up at Leiter's Legal Philosophy Blog, although in the latter case the debate was carried on at Brian's blog as well. For the record, I'm with Zangwill on the temptations of formalism. I think, in sundry ways and in different philosophical contexts, Stephen Toulmin, Hilary Putnam, Harold I. Brown, Martha Nussbaum, Michael Williams, Nicholas Rescher, John D. Norton [with regard to induction]. Richard W. Miller, and Deirdre McCloskey [in economics], among others, have done a fine job of articulating the reasons why we should be wary of the seductions of formalism: in Putnam's words, “This revolt against formalism is not a denial of the utility of formal models in certain contexts; but it manifests itself in a sustained critique of the idea that formal models, in particular, systems of symbolic logic, rule books of inductive logic, formalizations of scientific theories, etc.—-describe a condition to which rational thought can or should aspire.” In other words, our conceptions of rationality cast a net far wider than all that can be scientized, logicized, mathematized, in short, formalized: “The horror of what cannot be methodized is nothing but method fetishism.”

FWIW, my own sometime aversion to deontic logic is that I think the most well-known systems give substantively wrong results, and I am not all that interested in being a logic pioneer. E.g., according to me, it is not true that 'ought' applies most fundamentally to states of affairs, or that necessary states of affairs ought to be. In a formal system these appear as minor quirks, useful for getting the formalities right. But taken with philosophical seriousness I think they are deeply misleading. Geach has a paper about this called "Whatever Happened to Deontic Logic?" which is I think productive reading.

Resistance to deontic logic needn't be due to the acceptance of philosophical falsehoods, such as the neutrality of logic nor with the fact that a particular system of deontic logic is controversial. Rather such resistance is due to the conviction that extant systems seem to embody both false and misleading normative judgments. You may disagree. That's fine. But there is a genuine philosophical dispute here. Moreover it is not clear how doing deontic logic would help resolve this dispute. Rather it would seem what is required is, well, what we are doing already---reasoned philosophical investigation into the nature and reality of normative phenomena.

Not to be inflammatory or anything, but I think one reason why people mistrust deontic logic is that its proponents often seem less concerned with the data and more concerned with their system - a system which, though powerful and insightful in many respects, is also historically an extension of modal logic, rather than informed from the ground up by insights from ethics. It would not be terribly surprising if such a system turned out simply to have formalized some of the wrong things in order to successfully tell us how the sense of 'ought' in which moral philosophers investigate what we ought to do and why actually works. It doesn't follow that there is anything wrong with formal methods as such; the suspicion here is simply about the specific formal tools that have actually been applied.

I also think it's important to distinguish between formal semantics for normative concepts and deontic logic, two things which Ralph's post runs together. I do think it's important to pay attention to formal semantics, but one of my concerns with the deontic logic literature that I know, is that it doesn't pay enough attention to the question of how the sentences of the formal languages employed by the logic could be readings generated compositionally from the sentences of English which they are supposed to capture. The construction of a logic is the exercise of building a formal system in which there are sentences that are related in much like the ways that sentences of natural languages like English are related, and more elaborate systems do better at yielding parallels for each of the kinds of thing that we seem to be able to say in English. But this formal work isn't really formal semantics unless it is informed by the constraint that these readings have to be generated in some way by the words of the English sentence and how they are put together.

Thanks for all those comments! I started composing some replies, but then I just ran out of time (9 o'clock has just struck here in Oxford, and I'm teaching all day...). Anyway, this is as far as I got:

1. Patrick: I guess this is a deep methodological question. But this is what I think. Some use of formal methods is the only way to achieve the maximum level of precision, and philosophical inquiry ought to strive for the maximum possible level of precision. It would be unwarrantedly defeatist to announce in advance that no kind of precision that makes use of formal methods is possible. Of course, the more precise a claim is, the easier it is to see what it wrong with it! So when one is using formal methods, it is even harder to get things right than when one uses more informal methods. But that isn't a reason for not making the attempt.

2. Mark Kalderon: This is what I meant by 'deontic logic'. I meant to refer to any attempt to see if there are special logical principles (i.e. rules of consistency or entailment) that flow from the nature of the concepts that can be expressed in English by the words 'ought' or 'should'. Consider the analogy of modal logic, which as I see it tries to work out what logical principles flow from the nature of the concepts that can be expressed by 'must' or 'has to' and the like.

I don't think that this logical investigation is independent of substantive theorizing about (e.g.) metaphysical necessity, but it does seem to be a distinctive part of such theorizing. Someone might try to theorize about metaphysical necessity without looking at modal logic. But ideally they shouldn't. A theory about the distinctive logical properties of a concept is a crucial part of a good semantic theory of the concept. So it is a constraint on your theory about what 'must' means that it can yield a plausible story about which modal logic is correct for which sorts of 'must' and why. I say that the same is true for 'ought'.

3. Mark Schroeder. Of course, it might be that all the linguists and formal semanticists are wrong to think that 'ought' is broadly speaking a modal term. So it might be that the classical tradition of deontic logic is barking hopelessly up the wrong tree. Still, this wouldn't show that there is no sort of logic of 'ought' to be found.

E.g., some philosophers in the 1970's briefly flirted with the idea that in some uses 'must' and 'necessarily' are not propositional operators but predicate modifiers. Even they didn't say that we should draw the conclusion that there is no logic of 'must' to be found.

Of course, I do in fact think that 'ought' is broadly speaking a modal term, and that the classical tradition in deontic logic is broadly sound. To help it to deal satisfactorily with the linguistic data, it only needs to be enriched; it does not need to be junked. But I wasn't defending my specific view in this post. I was just lamenting the fact that so few metaethicists (with honourable exceptions at USC of course!) are attempting to engage with these issues at all.


I appreciate your response to my comment. As the quote from Putnam attests, I'm not against formal models as such (hence I would not--nor did not--argue that 'no kind of precision that makes use of formal methods is possible'), but I think reflection on the history of philosophy informs us that the precision of the sort sought by formal models has often by something of a pipe dream in philosophy, and that *clarity* and/or *systematization* are rather more modest and reasonable desiderata (apart from the fact that it is among a number of virtues and ends philosophical inquiry ought to strive for). In addition, I suspect the desire for precision is often part of the greater desire to make over the philosophical enterprise along the lines of this or that picture of science (hence Avrum Stroll's critique of scientism in philosophy) or mathematics in which precision is indeed one proper standard or goal and only sometimes (after Godel) attained. If we let epistemologists weigh in on this question (and not simply those enchanted with radical scepticism), I doubt many of them would see our epistemic practices or the normative explication of same as amenable to formalization. In fact, be it Rescher's recent elaboration of "presumptive" reasoning or Michael Williams' (after Brandom and others) elaboration of a Default and Challenge model of belief entitlement, or recent work in "epistemic contextualism," or focus on practical reasoning and the nature of judgment, we see decisive moves away from such formalization, inclusive of the sort of deductive certainty or demonstrative conception of knowledge which was long bewitched by the quest for formal *precision*. In different ways, the elaboration of non-classical forms of logic (paraconsistent, etc.); the appreciation of informal logic (Walton and others); nominalist leanings in ontological studies (Ian Hacking); the recognition that "forms of rationally are...interculturally available even if they are not always interculturally instantiated" (Jonardon Ganeri); the continued attraction of Wittegenstein's later work; the ethical approaches of, say, Dancy or Audi, the interest in narrative ethics (and storytelling in general, as in treatments of personal identity topics), or the broadening of "the ethical" (Joel Kupperman, Iris Murdoch...); non-realism in the philosophy of science (or avoidance of the realism debate altogether, as with Ronald Giere); elaboration of the role of the emotions vis-a-vis rationality (Nussbaum, Solomon, Ben-Ze'ev...); work in the philosophy of mind of late by Putnam, Descombes, Hutto, Bennett and Hacker, Auyang, et al.; pragamatics in the philosophy of language; a sophisticated appreciation of non-Western worldviews/philosophies (e.g., of Indic and Chinese provenance by the likes of Hansen, Ganeri, Siderits, Sorabji, Sen, Garfield, Chakrabarti, Kapstein, Fingarette...); the interest in non-propositional thought or awareness (not necessarily of the Russellian sort); "many worlds" metaphysics or metaphysical perspectivalism or pluralism a la Lewis, Lynch, the Jains or Dupre, for example (I'm assuming the denial of such pluralism is often correlated with a penchant for precision in metaphysics which, after all, lacks the 'messiness' and perspectivalism intrinsic to the brief on behalf of metaphysical pluralism); all serve as evidence that formalism increasingly is not, correctly I think, a preoccupation among philosophers, if not that the precision intrinsic to formalism is neither desirable nor attainable in much of the philosophical enterprise. But my constitutional pluralism (methodological and otherwise) would never rule out formalism in *some* endeavors and contexts. At any rate, and FWIW, this is my take on matters (from the outside looking in as it were).

Erratum: "...has often been something of...."

Hi Ralph,

I've got a question that the following exchange between you and Mark Kalderon has prompted:

Ralph: ...some of the contributors to this blog who have belittled the significance of formal deontic logic for legal philosophy have also gone on to claim that deontic logic has "a limited role in moral .... philosophy" as well. I confess to finding this claim quite shocking. Isn't it perfectly obvious that the study of the logic of 'ought' is part of metaethics, which is a crucial part of moral philosophy? ... it is a sort of diffidence about formal technicalities...

Mark: ...Rather [than doing deontic logic] it would seem what is required is, well, what we are doing already---reasoned philosophical investigation into the nature and reality of normative phenomena.

Ralph: This is what I meant by 'deontic logic'. I meant to refer to any attempt to see if there are special logical principles (i.e. rules of consistency or entailment) that flow from the nature of the concepts that can be expressed in English by the words 'ought' or 'should'.

My question: Does Bernard Williams therefore qualify as doing deontic logic in 'Ethical Consistency'? There he considers 'premisses or rules' such as 'ought implies can' and what he dubs 'the agglomeration principle'. He takes himself to be offering a 'logical reconstruction of moral conflict'. He claims that 'it is surely falsifying of moral thought to represent its logic as demanding that in a conflict situation one of the conflicting ought's must be totally rejected.' Etc. But the paper consists entirely of sentences in English (with the occasional foreign word or phrase thrown in). It is devoid of formal deontic logic.

In your original post, you refer to 'formal deontic logic' and its technicalities. But in your reply to Mark, you appear to cast the net more widely so that deontic logic encompasses what Williams is doing in 'Ethical Consistency'. So I think you're faced with the following dilemma:

If deontic logic is restricted to the formal, it's not clear that we need that, as opposed to what Williams is doing, in order to write about the logic of ought in a philosophically illuminating way.

If, however, you cast the net more widely (as you do in response to pressure from Mark), then it's just no longer truth that there's little interest in deontic logic among moral philosophers.

Mike, you write,

If deontic logic is restricted to the formal, it's not clear that we need that, as opposed to what Williams is doing, in order to write about the logic of ought in a philosophically illuminating way.

There is this problem. The deontic inferences considered intuitively valid in English might not all be valid in any consistent system. That's one good thing, I think, that formalization can provide. It can show you what else you're committed to given that you insist on this or that deontic closure principle. It can tell you what sorts of theses you have to abandon if you insist on the consistency of, say, OA & O~A. It can show what kinds of (so called) minimal models allow OA & O~A. etc. I don't think that can be done when working in English alone. Or, more cautiously, I don't think it can be as easily done English (or any natural language). One other good feature of the semantics of formal deontic languages that is often overlooked: It provides a clear interpretation of a language that does not always go smoothly into English. Lots of worries about deontic theses are just the result of a hasty interpretation in English.

On at least one larger question at issue, deontic logic is not much different from other interesting logics (logics of vagueness, belief, necessity, etc) in being philosophically controversial. There are all sorts of deontic logics (von Wright has one) on which 'O' is not a sentential operator, but a predicate taking actions as arguments. Castandeda has a dauntingly complicated one (operators festooned with indices) that he says solves every deontic paradox (well, you know), Richmond Thomason has a tensed deontic logic, and so on. They're definitely controversial, but as noted, so is every interesting logic.

Folks, I just wrote out a long post on deontic logic over at

which is where Ralph's original crosspost came from. It is long (did I mention that it is long?) and mostly directed at legal theory, rather than metaethics, so I won't crosspost myself, but it also contains some general babble about what is happening in deontic logic today that seems relevant to some of the comments here, so if you're interested, please help yourself.

(My general feeling is that deontic logic these days is much more data-driven and much less top-down and imperialistic than people on this thread seem to appreciate. There is no longer any sense of "Please take my modal system KD (or KD45) and represent your problem in it, and if that doesn't work, so much the worse for your problem." What's happening now is that people are trying to craft the tools necessary to represent normative reasoning of all sorts at a fine-grained level. Many proposals are no longer even modal at all.)

Whoops, pardon me, you've got to put an "l" at the end of the "htm" in the link in the previous post to get to the blog I mean to point at.

(I am defeated by the technology here - you can tell I'm a split appointment in computer science, right?)

I'll be the first to admit to both laziness and to not being very good at logic. But I have a great deal of respect for the less lazy and the logically more able.

It is partly because of this that I'm rather confident that those better at constructing formal models than I am will be able to construct good formal models for whatever comes out as a plausible theory of the entailments between moral claims involving oughts and the like. (Jeff H's comments above and his longer comment at the original venue for this discussion seem to me to support this confidence.) So I tend to think about the relatively simple issues (for example, do ought judgements represent a relation between agents and act-types, or are such judgements better represented in the more traditional way Ralph favors?).

There are a couple of reason for me to go on pursuing metaethics in this way: (1) It seems like the answer to these sorts of questions are more fruitfully thought of as constraints on the formal models than thinking of it the other way around. At least in my experience, when I overcome my laziness and work through the formal representation of various ideas, the key issues often turn on relatively simple but subtle points, as opposed to anything so far from the original assumptions built into the formal models that we need the formal apparatus to discover the implications of these assumptions. And (2) given my talents, such as they are, even if there are surprising results flowing from the models which can in turn be used to compare one model to the next for adequacy, someone like me isn't going to be the one who discovers those surprising results. I don't think this shows any disrespect for those like Jeff and Mark and Ralph who are obviously capable of doing more than I am by focusing on the logical models meant to capture entailments between ethical claims.

I suppose when I'm honest there is also a third reason for my reluctance to grant Ralph's point, one which is suggested by Mark S's comment above. It often seems to me that the papers which bring deontic logic to bear on issues of interest rule out substantive positions in moral semantics and metaphysics because the authors are taken with an analogy to the logic of possibility and necessity. Yet the analogy doesn't seem like it can bear the needed philosophical weight. When the people who rule out such positions on the basis of the analogy go on to accuse those who don't rule them out of making some sort of simple logical error it's easy to ignore the claims as a sort of posturing rather than a serious attempt to engage on the underlying issues. So maybe it would be helpful to hear some defense of the analogy.

This is a great set of comments. I'm not going to be able to respond to them all right now (I may try on the weekend). But one thought that occurred to me on reading these comments is this.

Of course Williams's discussion in "Ethical Consistency" about whether oughts "agglomerate" is a discussion of an issue in (informal) deontic logic. For many purposes (including Williams's purposes in that paper) such informal deontic logic is enough. However, I still think that for a full-blown semantic theory for the normative terms, one should aim for a more formal logical theory.

Why do so many people dislike deontic logic? Here's another suggestion (less inflammatory than my first ...):

The great pioneers of deontic logic (e.g. G.H. von Wright, Bengt Hansson, Lennart Aqvist, David Lewis, et al.) displayed tremendous acumen and subtlety in philosophical logic. But as Jeff Horty rightly says, they weren't sufficiently driven by the data of our actual intuitions about what people ought to do or think, or about how things ought to be. Since their theory wasn't clearly grounded in the data, it inevitably came to seem that their logical systems -- and especially SDL, aka KD -- are inadequately motivated, making it no surprise that these systems also seem to be plagued by all sorts of weird problems when it came to accounting for some pretty elementary data.

So a lot of philosophers were put off. What they don't realize is that there are many other possible approaches to deontic logic besides SDL, and those few hardy philosophers (like Jeff Horty, and to a lesser extent, myself) who persist in working on deontic logic, have tried hard to make sure that the logical systems that we try to develop that are more securely grounded in the intuitive data.

I hope that my first comment wasn't misunderstood as inconsistent with what Jeff and Ralph have just recently said - I personally couldn't be a bigger fan of Jeff's work, in particular, and think that it contains an awful lot for both normative ethicists and metaethicists to learn from. It is certainly deeply informed by data.

But if Ralph's original question was sociological, I do think that the best answer as to do with a perception that much work on deontic logic has involved shoe-horning of one sort or another. have to confess that (rightly or wrongly) I've sometimes felt this way about things Ralph says, myself!

One of the great things about formal methods, though, is that they allow a rigorous way of testing exactly what the costs are of any given way of trying to do things, and if there really is any shoe-horning going on, that's something that eventually shows up, and it's much easier to determine where to locate it. More dialogue is definitely worth encouraging.

Here's another actual problem I thought of. Most folks would agree that if you ought to perform some end, you ought to perform any necessary means to that end. But there is a significant difference in many people's minds between necessary means, necessary conditions, and necessary consequences. (Any necessary truth is a necessary condition though not a necessary means--in ordinary speech, I think; necessary consequences happen after the act, while means are simultaneous or prior. And what one wants to say about 'ought' in all these cases might well be different.) But the differences between means, conditions, and consequences are very hard to capture formally; one is tempted to just represent all of them with a conditional. So that's another area where it looks like progress is easier informally than formally.

All that said, I agree with several others that I have no intrinsic hostility to formal methods and they certainly have their uses.

fwiw, Paul McNamara has a very nice SEP entry covering some of the problems/advantages mentioned in the thread.

Ralph’s post, as always, is interesting but I’m a bit unmoved for reasons that overlap a bit with stuff others have said. Messages like this are, after all, legion. Summing up plausible specimens I've heard, no one can credibly practice moral philosophy who has not first rendered himorherself an expert on classical Greek philosophy (read in the original of course), Kant, Hegel, Marx, Nietzsche (all in German please), the broad canon of western literature, evolutionary biology, empirical psychology (a particularly popular focus for such tirades of late), welfare economics, formal decision theory and statistics, deontic logic and of course the whole of the rest of philosophy, metaphysics, epistemology etc. Which would be nice obviously and we all do our best. Some folks like Allan Gibbard seem to more or less pull it off. For most of the rest of us the flesh is just too weak and we shouldn't beat ourselves up too much. Even philosophers have to specialize and exploit the division of labour, bringing different skills and specialisms to the table. Like most of us I can’t claim to be more than a dilettante in most of the above areas. I don't make many forays into the psychological or economic journal literature, for example. But I do read some material by fellow philosophers who do make such forays and rely on them to bring me news of anything very exciting happening there relevant to my own concerns. I’m not terribly repentant: that’s not laziness, just how science and scholarship, as collective enterprises, are meant to work. With formal deontic logic it’s much the same. And is there, anyway, so much news? No one who hasn't mastered and understood Godel's incompleteness theorem can be a terribly serious philosopher of maths; plausibly any serious political philosopher should jolly well have understood and reflected on Arrow's theorem and anyone planning to specialize in philosophy of language better get to grips with Tarski’s work on truth. But are there really any results of comparable depth and philosophical relevance that formal deontic logic has been cooking up while none of us have been looking? If so, Ralph's case is best made by spreading the news. If not...

Jimmy -- I wasn't saying that there are "results" in deontic logic that need to be absorbed by all moral philosophers.

What I was saying was this. Surely everyone would accept that a full semantic account of the meaning of modal terms like 'must' and 'can' should say something about which modal logic is the right logic for each of the concepts that these modal terms can express, and why. I would regard any semantic account of such terms that just said nothing about modal logic as fairly obviously incomplete.

It seems overwhelmingly plausible to me that the same is true for deontic terms. Practically every linguist whom I have talked to is astonished to learn that many metaethicists reject their assumption that the term 'ought' is itself a modal term. Now it might be that all these linguists are utterly mistaken, but I take it that their view should be taken seriously. We should conclude no semantic account of the meaning of 'ought' could be complete if it just says nothing about deontic logic. (So, yes, I do regard it as a quite serious flaw in Gibbard's Thinking How to Live that it says basically nothing about deontic logic.)

As I have already remarked, I'm at a loss to understand why any metaethicist who is interested in the semantics of words like 'ought' would disagree with what I just said. Perhaps these metaethicists just have a profoundly mistaken conception of what a semantic theory -- including a semantic theory for terms like 'ought' -- is all about?

"We should conclude no semantic account of the meaning of 'ought' could be complete if it just says nothing about deontic logic. (So, yes, I do regard it as a quite serious flaw in Gibbard's Thinking How to Live that it says basically nothing about deontic logic.)"

I guess my reaction to this would just amount to broad agreement with the thrust of what Mike Otsuka says above. In a broad sense of logic incorporating the relatively informal your first sentence is perhaps as truistic as you want us to believe but your charge against Gibbard is then surely unjust: in that broad sense, surely the whole of Parts 2 and 3 of THTL are about little else.

Pea Soup is almost as good as Facebook for distracting me when I should be writing lectures on the Meno.

That's the Pea Soup motto -- we are almost as distracting as facebook!

Ralph,I have a simple clarificatory question.
What would you say to someone who makes the following speech:

"I agree that to have a complete meta-ethical theory, we ought to say something about the 'logic' of the concepts of obligation (O) and permissibility (P). That is we should determine whether there are special principles (i.e. rules of consistency or entailment) that flow from the nature of these concepts. And of course there are. They consist in the following axioms, and theorems deriviable from them:

O(p) iff ~P(~p)
O(p) -> P(p)
If Necessarily (p iff q) then O(p) iff O(q)

No other "axioms" featuring these concepts are *logical* or analytic principles, but rather are synthetic principles discoverable only by substantive ethical theorizing."

Is this person failing to take deontic logic seriously in your sense? What methodological mistake is he making?

1. Kris -- The person whom you envisage would be certainly taking deontic logic seriously! But in view of how many objections philosophers have raised against the logical principles that you enumerate, and in view of the arguments that various other philosophers have given in favour of acknowledging other logical principles besides the ones that you enumerate, this person should probably say a bit to defend or justify his or her view!

2. Jimmy -- Perhaps my memory of Gibbard's book has already got hazy, but I actually remember finding it pretty unclear what answer his theory would imply to some fairly basic logical questions. E.g., is 'ought' a propositional operator, or is it a predicate applying to triples consisting of an agent, a time and a mental state or action? Do sentences in which 'ought' has largest scope allow the intersubstitution of logically equivalent terms? Does 'ought' agglomerate over conjunction? Does it distribute over conjunction? Etc.. (Perhaps I'll have another look at Parts II and III of his book to see if I have forgotten anything.)

That is we should determine whether there are special principles (i.e. rules of consistency or entailment) that flow from the nature of these concepts. And of course there are. They consist in the following axioms, and theorems deriviable from them:
O(p) iff ~P(~p)
O(p) -> P(p)
If Necessarily (p iff q) then O(p) iff O(q)

Kris, I know the question is not directed to me, but I'll say one thing. There are weak, non-Kripkean deontic logics that do not validate all of those, and I'm not sure we could know a priori how weak the correct deontic logic should be (or even if there is such a thing). One point that gets noted all of the time is that as you weaken the logic, you increase the number of theses that are non-equivalent. That is, you increase the number of distinctions your logic recognizes. In SDL, I'm pretty sure OA -> PA is provably equivalent to ~(OA & O~A), though those principles sure seem to express diffeent propositions. That's one reason to go weaker; the logic is conflating important distinctions we recognize when reasoning in English. But this is the same question that is raised for alethic logics, viz. what is the correct logic of necessity? It seems like a question in philosophical logic.

Mike -- We don't need full-strength SDL to prove the logical equivalence of OA -> PA and ~(OA & O~A) (at least so long as the conditional in the first proposition is a simple material conditional).

All we need is classical truth-functional logic, plus the principle that 'PA' logically implies '~O~A'.

Some deontic logicians have denied that 'PA' logically implies '~O~A'. But surely an easier way to capture your sense that the two propositions are different would be to deny that logically equivalent propositions are identical?

Some deontic logicians have denied that 'PA' logically implies '~O~A'. But surely an easier way to capture your sense that the two propositions are different would be to deny that logically equivalent propositions are identical?

Sure, that's one way. But, ugh, things get much messier when P's proposition is not just [P]. In any case, I didn't mean to express a view dear to me about the equivalences in SDL. It was just an example. I should know better. I keep forgetting you're an SDL defender!!

But surely an easier way to capture your sense that the two propositions are different would be to deny that logically equivalent propositions are identical?

Ralph, just a quick point. The problem I alluded to is not that logically equivalent propositions are identical. If this were the problem, then every theorem would express the same proposition. I'm actually not entirely unhappy with that, but others are. The problem I was pointing to was with provable equivalence. I can't prove axioms from axioms in SDL, but I can prove ~(OA & O~A) from OA-->PA and vice versa. I can also prove that there is no difference between prohibition dilemmas and obligation dilemmas. But you may not want those equivalences as theorems. Some have denied this particular equivalence, for instance, on intuitive grounds (Peter Vallentyne, I seem to recall, has argued that the former are possible, though not the latter). Anyway, Peter Schotch & R.E. Jennings give these sorts of reasons for preferring a weaker logic. 'Non-Kripkean Deontic Logic' in R. Hilpinen's New Studies.

Mike - I'm not quite sure what you mean.

What can be proved from what always depends on the background logic. In practically all logics (except for a few weird relevance logics I guess), you can always introduce an axiom anywhere into any proof. And so axioms can be proved from axioms -- trivially -- since axioms can be proved from anything whatsoever! Anyway, in any logic that is complete, logical equivalence just is provable equivalence.

At all events, if you doubt that ~(OA & O~A) and OA -> PA are provably equivalent, and you don't want to tamper with classical truth-functional logic, you will have to reject the idea that PA is equivalent to ~O~A.

Hi Ralph,

I'll just give an example. In SDL, we can prove that PT (T = tautology, P = permissible) is equivalent to PA v P~A, on the basis of CP. P(A v B) -> (PA v PB) and the rule RPM. |-A -> B / |-PA -> PB (the nomenclature is from Chellas). Suppose you don't think the initial equivalence is correct. One natural thing to do is move to weaker logic that invalidates CP or RPM. In that non-normal logic you cannot prove one from the other. I'm not sure which among those weaker logics is complete, but it shouldn't be too difficult to find out. If the relevant one's are, then your point it taken. My point was just to note that we do not know a priori (i.e. from the concept of permission or obligation, say) that the correct logic is not among the weaker ones.

What Mr.Nick Zangwill has stated in regard to meta-ethics and deontic logic not applying---is
relativist/anti-foundationalist hogwash !

Deductive logic when properly applied is indeed quite infalliable. Zangwill cites the work of Quine as supposed ballast for the false thesis that logic is somehow supposedly inherently "limited". Much of the epistemology of Quine is predicated on a notion called 'meaning holism'. Mening holism has been quite discredited by the ground-breaking work of Lawrence Kaye ---who at the 'Epistemology Papers By Subject' website wrote a brilliant article on how to avoid holism . In the article, Lawrence Kaye, with data culled from computer systems and cognitive studies, showed that Quine was wrong when Quine claimed that every act of understanding was spread over a web of belief . He showed that acts of knowledge can be atomic and NOT spread out over a web of belief ...that Quine was wrong to think that every cognitive act was intertwined with every other belief that a person has !

Thus the anti-logic position that Zangwill is taking being predicated on the holism that is the underpinning of the epistemology of Quine can be shown to be founded on a flimsy base .

Contrary to popular opinion, there are NOT two or more sides to every isssue . Indeed reason is the final arbiter of all Truth !

NOTE TO Patrick O'Connell ,

In regard to the statement , "or mathematics in which precision is indeed one proper standard or goal and only sometimes (after Godel) attained" , you ,sir, apparently have fallen for the hype that claims that Godel's so-called "proof" indicates that is inherently impossible to have a formal system of mathematics that is both complete and consistent . That is yet another example of misleading hype that the relativist/ANTI-foundationalist/ postmodernist crowd has touted and one which is quite false .

The mathematician Gerhard Gentzen apparently showed with 'Gentzen's Proof' some time after Godel published the so-called Godel's Proof that the completeness consistency of mathematical axioms CAN indeed be demonstrated by transfinite induction . Godel's so called "proof" has shown to be quite hyped , and NOT the trump card against formalist precision that the relativist crowd loves to claim . Apparently Prezburgers arimathetic ---a mathematical system of axioms having to do with adding can be shown to be both complete and consistent also .

The claims of those who cry "paradox" are shown to be hype .

Indeed the utmost precision is a fundamental requirement of authentic philosophy . As Descartes explained philosophy is about distinct ideas . Tolerating even a little ambiguity is ANTI-philosophy ! It is the height of intellectual laziness and depravity to settle for even a partial relativism that accepts anything less than the utmost formalized precision . It is a lazy mind which *refuses* to split hairs .

It is incumbent on all those who seek philosophy to never sell-out , but to insist on the utmost precision .

So-called "paraconsistent logic" is an oxymoron . So-called paraconsistent logic is obscurantist baloney ; balderdash !

Without rigid consistency anti-climatic thought reigns .

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